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Math Help - Integration/Derivative problem

  1. #1
    Member CalcGeek31's Avatar
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    Integration/Derivative problem

    The Acceleration of an object is given by a(t)=6sin(t) with initial velocity of -9.5(v(0) = -9.5). Find the distance the object travels on the interval [0,pi] to the nearest integer.

    I was able to take the integral of the acceleration to get it to the velocity and I found C(the number that when you take the integral it ends up at the end) but I am not sure how to continue. I assume you take another integral but I am not sure.

    Could you please explain?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by CalcGeek31 View Post
    The Acceleration of an object is given by a(t)=6sin(t) with initial velocity of -9.5(v(0) = -9.5). Find the distance the object travels on the interval [0,pi] to the nearest integer.

    I was able to take the integral of the acceleration to get it to the velocity and I found C(the number that when you take the integral it ends up at the end) but I am not sure how to continue. I assume you take another integral but I am not sure.

    Could you please explain?
    After you found C, you were able to obtain v(t). Now, you need to find \int_0^\pi v\left(t\right)\,dt.

    Can you take it from here?
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  3. #3
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    s = v*t
    if v (= velocity) is constant.

    s = v1*delta_t1 + v2*delta_t2 + ...
    where v1 is constans during the timeinterval delta_t1

    s = integral(t_ini to t_fin) v(t)*dt
    if the velocity is a function in t.

    So, you're right!
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  4. #4
    Member CalcGeek31's Avatar
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    I believe I can but I was wondering if my velocity function was correct I apologize for not mentioning it originally,

    I got v(t)= -6cos(t) - 3.5
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  5. #5
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    Quote Originally Posted by CalcGeek31 View Post
    I believe I can but I was wondering if my velocity function was correct I apologize for not mentioning it originally,

    I got v(t)= -6cos(t) - 3.5
    Correct.
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